Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves

In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived cylindrical(spherical) KdV and mKdV equations. Being aware of the fact that there exists no exact analytical solution for the progressive waves for such evolution equations we presented the exact analytical solution of a generalized form of such evolution equations in the planar geometry and used this solution to obtain an analytical approximate progressive wave solution to the generalized evolution equation. Then the progressive wave solutions for the cylindrical(spherical) KdV and m-KdV equations is obtained as some special cases. The analytical approximate solutions so obtained are compared with the numerical solutions of these equations. The results reveal that both solutions are in a good agreement. One advantage of present analytical approximate solution is that it allows readers to gain information, share understandings, or carry out a physical parametric study on the evolution solution behavior as well as the solution calculation has no CPU time-consuming or round off error.